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/*
ARPACK++ v1.2 2/18/2000
c++ interface to ARPACK code.
MODULE RSymGReg.cc.
Example program that illustrates how to solve a real symmetric
generalized eigenvalue problem in regular mode using the
ARrcSymGenEig class.
1) Problem description:
In this example we try to solve A*x = B*x*lambda in regular mode,
where A and B are obtained from the finite element discretization
of the 1-dimensional discrete Laplacian
d^2u / dx^2
on the interval [0,1] with zero Dirichlet boundary conditions
using piecewise linear elements.
2) Data structure used to represent matrices A and B:
ARrcSymGenEig is a class that requires the user to provide a
way to perform the matrix-vector products w = OPv = inv(B)*A*v
and w = B*v. In this example a class called SymGenProblemA was
created with this purpose. SymGenProblemA contains a member
function, MultOPv(v,w), that takes a vector v and returns the
product OPv in w. It also contains an object, B, that stores
matrix B data. The product Bv is performed by MultMv, a member
function of B.
3) The reverse communication interface:
This example uses the reverse communication interface, which
means that the desired eigenvalues cannot be obtained directly
from an ARPACK++ class.
Here, the overall process of finding eigenvalues by using the
Arnoldi method is splitted into two parts. In the first, a
sequence of calls to a function called TakeStep is combined
with matrix-vector products in order to find an Arnoldi basis.
In the second part, an ARPACK++ function like FindEigenvectors
(or EigenValVectors) is used to extract eigenvalues and
eigenvectors.
4) Included header files:
File Contents
----------- -------------------------------------------
sgenprba.h The SymGenProblemA class definition.
arrgsym.h The ARrcSymGenEig class definition.
rsymgsol.h The Solution function.
5) ARPACK Authors:
Richard Lehoucq
Kristyn Maschhoff
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#include "arrgsym.h"
#include "sgenprba.h"
#include "rsymgsol.h"
template<class T>
void Test(T type)
{
// Creating a pencil.
SymGenProblemA<T> P(100); // n = 100.
// Creating a symmetric eigenvalue problem and defining what we need:
// the four eigenvectors with largest magnitude.
ARrcSymGenEig<T> prob(P.A.ncols(), 4L);
// Finding an Arnoldi basis.
while (!prob.ArnoldiBasisFound()) {
// Calling ARPACK FORTRAN code. Almost all work needed to
// find an Arnoldi basis is performed by TakeStep.
prob.TakeStep();
if ((prob.GetIdo() == 1)||(prob.GetIdo() == -1)) {
// Performing w <- OP*v.
// In regular mode, this product must be performed
// whenever GetIdo is equal to 1 or -1. GetVector supplies
// a pointer to the input vector, v, and PutVector a pointer
// to the output vector, w.
P.MultOPv(prob.GetVector(), prob.PutVector());
}
else if (prob.GetIdo() == 2) {
// Performing w <- B*v.
P.B.MultMv(prob.GetVector(), prob.PutVector());
}
}
// Finding eigenvalues and eigenvectors.
prob.FindEigenvectors();
// Printing solution.
Solution(prob);
} // Test
int main()
{
// Solving a single precision problem with n = 100.
Test((float)0.0);
// Solving a double precision problem with n = 100.
Test((double)0.0);
} // main
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